Comparing IRR on Projects

Project X has an internal rate of return (IRR) of 14%. Project Y has an IRR of 17%. Both projects have conventional cash flow patterns (all inflows after the initial cash outflow). If the required rate of return is:

A.14%, the net present value (NPV) of Project Y will exceed the NPV of Project X.

B. greater than 17%, Project Y will have a shorter payback period than Project X.

C. 10%, both projects will have a positive NPV, and the NPV of Project Y will exceed the NPV of Project X.

Answer: A

Explanation: We know that at a 14% discount rate, the NPV of Project X is zero and the NPV of Project Y is greater than zero. There is no well-defined relationship between the required rate of return and ordinary payback. If Project Y is smaller in size, its NPV may be smaller than that of Project X.

From my understanding answer A or C is correct. Answer A because of the explanation given above. Answer C because a required rate of return of 10% is less than both the IRR of Project X and Project Y, thus they will both have a positive NPV. Plus, “Project Y will exceed the NPV of Project X.” because Project Y has a higher IRR than Project X. I’m guessing I’m missing something because it seems too blatant to me that both answers could be correct.

We can’t tell which project has a higher NPV at any RROR less than 14%. It all depends on the slope of the NPV profile. If the NPV profile for project Y is steeper than for project X, its NPV will be higher at ALL required rates. If it’s flatter, the two profiles MIGHT cross (but they might not).

The steepness of a project’s NPV profile is dependent on when the cash flows of the project occur - basically on the “duration” of the project (although the concept is used in a Fixed income setting, it applies here). If the project’s cash flows are “front loaded”, its NPV won’t change much as the RROR changes (i.e. the project will have a lower “duration”). OTOH, if the cash flows are more “back loaded” (they occur later in the project), the NPV profile will be steeper.